# Square metal sheet

Four squares of 300 mm side were cut out from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.

Result

f =  0.265
p =  26.5 %

#### Solution:

$a = 0.7 \ m \ \\ b = 300 \ mm = 300 / 1000 \ m = 0.3 \ m \ \\ \ \\ S_{ 1 } = a^2 = 0.7^2 = \dfrac{ 49 }{ 100 } = 0.49 \ m^2 \ \\ S_{ 2 } = 4 \cdot \ b^2 = 4 \cdot \ 0.3^2 = \dfrac{ 9 }{ 25 } = 0.36 \ \\ \ \\ o = S_{ 1 }-S_{ 2 } = 0.49-0.36 = \dfrac{ 13 }{ 100 } = 0.13 \ m^2 \ \\ f = \dfrac{ o }{ S_{ 1 } } = \dfrac{ 0.13 }{ 0.49 } = \dfrac{ 13 }{ 49 } \doteq 0.2653 = 0.265$
$p = 100 \cdot \ f = 100 \cdot \ 0.2653 = \dfrac{ 53 }{ 2 } = 26.5 = 26.5 \%$

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